onsider the triangle to the right.

Question

a. Write an equation that can be used to find the value of y.
b. What is mangle∠​K?
Upper LL
Upper MM
Upper KK
56 degrees56°
left parenthesis 5 y minus 19 right parenthesis degrees(5y−19)°

Question content area bottom
Part 1
a. Write the equation below.
5 y minus 19 equals 565y−19=56
​(Do not simplify. Do not combine like​ terms.)
Part 2
b. What is mangle∠​K?

Answer 1

To solve the problem, we first analyze the information presented:

1. It mentions the angle measure $\mathrm{\angle }K$ along with $(5y-19{)}^{\circ }$ and ${56}^{\circ }$.
2. Typically, in a triangle, the sum of the angles must equal ${180}^{\circ }$.

Part 1:

We are tasked with writing an equation to find the value of $y$. Considering the angle measures given and understanding that they are part of a triangle, we can use the equations provided.

To find $y$, we can set up the equation as provided:

$$5y-19=56$$

Part 2:

To find $\mathrm{\angle }K$, we only need the expression for $\mathrm{\angle }K$ if we substitute the value of $y$.

Starting with the equation we wrote:

1. From the equation: $$5y-19=56$$

2. Solve for $y$: $$5y=56+19$$ $$5y=75$$ $$y=15$$

3. Finding $\mathrm{\angle }K$: Now we substitute $y$ back into $\mathrm{\angle }K$: $$\mathrm{\angle }K=5y-19$$ Substituting $y=15$: $$\mathrm{\angle }K=5(15)-19=75-19={56}^{\circ }$$

Thus:

• The answer to Part 1 is: $$5y-19=56$$

• The answer to Part 2 is: $\mathrm{\angle }K={56}^{\circ }$